The unit can use 5v-30v depending on your parts you picked out. If you had 600 ohm beirs then 9v isnt good enough and you would have made a 30v unit. On the other hand if you had 16-32 cans then 9v is enough for you to go deaf
So no you are not limited to a 9v battery
Wall on the board refers to a external unregulated power source that is higher in voltage then your battery. Wall runs thru a diode and UC1 regulator to both power the unit and charge the battery.
If your going to make one without abattery, then soldering your power supply to wall is a good idea.
However soldering a battery to wall is a bad idea. It will go dead pretty quickly.
Solder your outs to OL,OR,OG. Output left, output right, and output groud. Dont let output ground touch chassis ground.
Solder your inputs to InputsiL,InputsiR,InputsiG. They are in one spot in the middle labeled IL,IR,IG.